Conventionally, in an RF (Radio Frequency) receiver for the radio communication systems such as a wireless LAN (Local Area Network) and a mobile telephone, a Low-IF (Low-Intermediate Frequency) system is applied frequently. In recent years, application of a bandpass ΔΣAD (Delta Sigma Analog to Digital) modulator to such a Low-IF system receiver has been discussed.
One of application examples of the bandpass ΔΣAD modulator to a Low-IF system receiver includes a technique that uses two real bandpass ΔΣAD modulators (one-input one-output). In this technique, not only the signal component but also the image component of an input signal is subjected to AD conversion in the real bandpass ΔΣD modulator. Hence, this technique has such a problem as power consumption increases which is inefficient.
As a technique to solve the above-mentioned problem, application of a complex bandpass ΔΣAD modulator with two-input and two-output to a Low-IF system receiver is proposed (for example, see Patent Documents 1 to 4). The transfer function of a complex bandpass ΔΣAD modulator is designed so that asymmetric spectral characteristics can be obtained for a DC region (direct-current region) and only the signal component is subjected to AD conversion. Therefore, when a complex bandpass ΔΣAD modulator is used, a high SQNDR (Signal to Quantization Noise and Distortion Ratio) can be obtained with low power consumption and a highly efficient AD conversion may be made.
Here, the configuration and characteristics of a general complex bandpass ΔΣAD modulator are explained with reference to the drawings. FIGS. 14 and 15 show a schematic circuit configuration of a complex bandpass ΔΣAD modulator. FIG. 14 is a diagram showing the signal flow of a complex bandpass ΔΣAD modulator and FIG. 15 is a diagram showing the configuration of a complex bandpass ΔΣAD modulator more specifically.
As shown in FIG. 14, a complex bandpass ΔΣAD modulator 300 is configured mainly by a subtraction unit 310, a complex bandpass filter 320, an analog-to-digital converter 330 (hereinafter, referred to as an ADC unit), and a digital-to-analog converter 340 (hereinafter, referred to as a DAC unit). Normally, the complex bandpass filter 320 is configured by connecting cascade integrator circuits including an operational amplifier. The connection relationship of each unit is described below.
The input terminal of the subtraction unit 310 is connected to the input terminal (not shown) of an input complex signal X(z) (hereinafter, simply referred to as an input signal X(z)) input from the outside and the output terminal of the DAC unit 340, and the output terminal of the subtraction unit 310 is connected to the input terminal of the complex bandpass filter 320. The output terminal of the complex bandpass filter 320 is connected to the input terminal of the ADC unit 330. Then, the output terminal of the ADC unit 330 is connected to the output terminal (not shown) of an output signal Y(z) and the input terminal of the DAC unit 340.
As shown in FIG. 15, the circuit in the complex bandpass ΔΣAD modulator 300 is separated into a channel 301 in which an in-phase component Iin of the input signal X(z) is processed (hereinafter, referred to as an I-channel) and a channel 302 in which an orthogonal component Qin is processed (hereinafter, referred to as a Q-channel). Thus, the subtraction unit 310 is configured by two subtractors 311 and 312 arranged in the I-channel 301 and the Q-channel 302, respectively. The ADC unit 330 is configured by two AD converters (quantizers) 331 and 332 arranged in the I-channel 301 and the Q-channel 302, respectively. Further, the DAC unit 340 is also configured by two DA converters 341 and 342 arranged in the I-channel 301 and the Q-channel 302, respectively.
In the complex bandpass ΔΣAD modulator 300, the signal X(z) (=Iin+jQin: j is an imaginary number) in a complex form including the in-phase component Iin and the orthogonal component Qin is input and the signal Y(z) (=Iout+jQout) in a complex form including an in-phase component Iout and an orthogonal component Qout is output from the complex bandpass ΔΣAD modulator 300. X(z) and Y(z) in FIG. 14 represent continuous input and output signals which have been subjected to z conversion, respectively. A variable z is represented by the following formula.z=exp(j2ωTs)=exp {j2π(Fin/Fs)}  Formula 1
Here, Ts in Formula 1 described above is a sampling period, Fs is a sampling frequency, and Fin is an input signal frequency.
If it is assumed that a transfer function of the complex bandpass filter 320 is H(z) and a quantized noise of the ADC unit 330 is E(z)=EI+jEQ, the output signal Y(z) is represented by the following formula.
                    ⁢          Formula      ⁢                          ⁢      2                  Y      ⁡              (        z        )              =                            I          out                +                  j          ⁢                                          ⁢                      Q            out                              =                                                  H              ⁡                              (                z                )                                                    1              +                              H                ⁡                                  (                  z                  )                                                              ⁢                      (                                          I                in                            +                              j                ⁢                                                                  ⁢                                  Q                  in                                                      )                          +                              1                          1              +                              H                ⁡                                  (                  z                  )                                                              ⁢                      (                                          E                l                            +                              j                ⁢                                                                  ⁢                                  E                  Q                                                      )                              
A coefficient 1/{1+H(z)} of the second term on the right side in the above formula 2 is a transfer function for the quantized noise E(z) and referred to as a noise transfer function NTF. The complex bandpass ΔΣAD modulator 300 is designed such that the zero point of the noise transfer function NTF(z) (the solution of z that satisfies NTF(z)=0) is generated within the frequency band of the signal component of the input signal, that is, the quantized noise E(z) is attenuated in the frequency band of the signal component. Such a technique as to adjust (design) the noise transfer function NTF(z) so that the quantized noise E(z) is attenuated in a desired frequency band is referred to as a noise shape technique.
For example, in order to perform the noise shape such that the quantized noise E(z) is attenuated in a band in the vicinity of Fin/Fs0.25, to which the frequency band of the signal component (hereinafter, referred to as a signal band) is set, the design is made so that the noise transfer function satisfies NTF(z)=(1−jz−1)N, that is, the zero point of the noise transfer function NTF(z) satisfies z=j (corresponding to Fin/Fs=0.25, see Formula 1 described above). Here, N is the order of the modulator, and an integer of 1 or more.
FIG. 16 shows an example of output power spectra of the complex bandpass ΔΣAD modulator 300 designed as described above. The horizontal axis in FIG. 16 represents the frequency, which is the input signal frequency Fin normalized by the sampling frequency Fs, and the vertical axis represents the level of the output power of the complex bandpass ΔΣAD modulator 300. Further, FIG. 16 shows spectral characteristics in a range of Fin/Fs=0.5 to −0.5. As is obvious from FIG. 16, by designing the complex bandpass ΔΣAD modulator 300 as described above, noises are reduced in the vicinity of Fin/Fs=0.25 (signal band).
As a complex bandpass ΔΣAD modulator having a configuration other than that shown in FIG. 14, conventionally, for example, a feed-forward type complex bandpass ΔΣAD modulator is proposed (for example, see Non-Patent Document 1). A schematic configuration of the feed-forward type complex bandpass ΔΣAD modulator is shown in FIG. 17. The same reference numerals that designate corresponding members in the complex bandpass ΔΣAD modulator 300 shown in FIG. 14 are used in FIG. 17. In this type, an addition unit 430 is provided between a complex bandpass filter 420 and the ADC unit 330, and the input signal X(z) of a complex bandpass ΔΣAD modulator 400 and an output signal of the complex bandpass filter 420 are added by the addition unit 430. In the complex bandpass ΔΣAD modulator 400 having such a configuration, it is also possible to obtain the same output power spectra as those in FIG. 16 by appropriately designing the transfer function H(z) of the complex bandpass filter 420.
Further, a noise-coupling type complex bandpass ΔΣAD modulator has been also proposed conventionally (for example, see Non-Patent Documents 2 and 3). A schematic configuration of the noise-coupling type complex bandpass ΔΣAD modulator is shown in FIG. 18. The same reference numerals that designate corresponding members in the complex bandpass ΔΣAD modulator 300 shown in FIG. 14 are used in FIG. 18. A noise-coupling type complex bandpass ΔΣAD modulator 500 includes a noise extraction circuit unit 540 configured to extract a quantized noise of the ADC unit 330 and feeds back the extracted quantized noise to the input side of the ADC unit 330 (inputs to an addition unit 530). Incidentally, when the extracted quantized noise is input to the addition unit 530, the signal is inverted before input. In this type of complex bandpass ΔΣAD modulator 500, it is possible to increase the order of the modulator in the signal band without increasing the number of stages (the number of operational amplifiers) of the integrator circuit in a complex bandpass filter 520. Thus, a higher-order AD conversion is made with low power consumption.
However, in the actual circuit of the various types of complex bandpass ΔΣAD modulators described above, there exist variations in capacitance in the circuit. Hence, a mismatch between the I-channel in which the in-phase component Iin of the input signal is processed and the Q-channel in which the orthogonal component Qin is processed (deviation in amplitude or phase between signals) is created. If a mismatch is created between I- and Q-channels, a complex conjugate of the frequency response is caused and a quantized noise of the image component is produced in a desired signal band (a quantized noise of the image component enters into a desired signal band). As a result, such a problem as SQNDR is reduced in the signal band is caused. Here, this problem is explained more specifically.
In FIG. 19, an equivalent circuit of a complex bandpass ΔΣAD modulator when a mismatch is created between I- and Q-channels is shown. An example in which a mismatch between I- and Q-channels in the complex bandpass ΔΣAD modulator shown in FIG. 15 is created is shown in FIG. 19. In FIG. 19, the same reference numerals that designate corresponding members in the complex bandpass ΔΣAD modulator 300 shown in FIG. 15 are used.
Here, a case is considered, where the signal amplitude of the in-phase component is larger than a predetermined amplitude by an amount corresponding to an amount of mismatch α and the signal amplitude of the orthogonal component is smaller than a predetermined amplitude by an amount corresponding to the amount of mismatch α. This mismatch is represented by integration blocks 351 and 352 provided in the I- and Q-channels in FIG. 19, respectively. In this case, the output signal Y(z)=Iout+jQout is represented by the following formula.
                                          I            out                    +                      j            ⁢                                                  ⁢                          Q              out                                      =                                                            H                +                                                      (                                          1                      -                                              α                        2                                                              )                                    ⁢                                      H                    2                                                                              1                +                                  2                  ⁢                  H                                +                                                      (                                          1                      -                                              α                        2                                                              )                                    ⁢                                      H                    2                                                                        ⁢                          (                                                I                  in                                +                                  j                  ⁢                                                                          ⁢                                      Q                    in                                                              )                                +                                                    α                ⁢                                                                  ⁢                H                                            1                +                                  2                  ⁢                  H                                +                                                      (                                          1                      -                                              α                        2                                                              )                                    ⁢                                      H                    2                                                                        ⁢                          (                                                I                  in                                -                                  j                  ⁢                                                                          ⁢                                      Q                    in                                                              )                                +                                                    1                +                H                                            1                +                                  2                  ⁢                  H                                +                                                      (                                          1                      -                                              α                        2                                                              )                                    ⁢                                      H                    2                                                                        ⁢                          (                                                E                  l                                +                                  j                  ⁢                                                                          ⁢                                      E                    Q                                                              )                                +                                                    α                ⁢                                                                  ⁢                H                                            1                +                                  2                  ⁢                  H                                +                                                      (                                          1                      -                                              α                        2                                                              )                                    ⁢                                      H                    2                                                                        ⁢                          (                                                E                  l                                +                                  j                  ⁢                                                                          ⁢                                      E                    Q                                                              )                                                          Formula        ⁢                                  ⁢        3            
When a mismatch is created between I- and Q-channels, on the right side of Formula 3 described above that represents the output signal Y(z), the term of the image component (Iin−jQin) of the input signal and the term of the image component (EI−jEQ) of the quantized noise appear. These image components enter into the signal band and cause the reduction in SQNDR of the signal component as is shown in FIG. 20.
FIG. 20 shows an example of the output power spectra of the complex bandpass ΔΣAD modulator when a mismatch is created between I- and Q-channels. The horizontal axis in FIG. 20 represents the normalized frequency Fin/Fs and the vertical axis represents the output power level. In the example in FIG. 20, the design is made so that the noise transfer function NTF(z) of the complex bandpass ΔΣAD modulator satisfies NTF(z)=(1−jz−1)N. Thus, in the range of the normalized frequency Fin/Fs=0.5 to −0.5 shown in FIG. 20, the signal band is in the vicinity of the Fin/Fs=0.25 like the example in FIG. 16 and the frequency band of the image component (hereinafter, referred to as an image band) is in the vicinity of Fin/Fs=−0.25.
As is obvious from FIG. 20, when a mismatch is created between I- and Q-channels, the noise level increases in the image band (in the vicinity of Fin/Fs=−0.25). As a result, the noise level in the signal band (in the vicinity of Fin/Fs=0.25) also increases, and SQNDR in the signal band is reduced.
In order to solve the problem of the mismatch between I- and Q-channels described above, a technique, in which a complex bandpass ΔΣAD modulator is configured such that the zero point of the noise transfer function NTF(z) is generated not only in the signal band but also in the image band (for example, see Non-Patent Document 4), has conventionally been proposed. Specifically, in Non-Patent Document 4, the above-mentioned problem is solved by separately providing an integrator circuit (including an operational amplifier) in the complex bandpass ΔΣAD modulator to generate the zero point (attenuation pole) in the image band.
FIG. 21 shows the gain characteristics of the noise transfer function NTF(z) of the complex bandpass ΔΣAD modulator proposed in Non-Patent Document 4. The horizontal axis in FIG. 21 represents the normalized frequency and the vertical axis represents the gain of the noise transfer function NTF(z). In the example in FIG. 21, the normalized frequency of the signal band is in the vicinity of 0.5 and the image band is in the vicinity of −0.5.
In the complex bandpass ΔΣAD modulator in Non-Patent Document 4, because the zero point of the noise transfer function NTF(z) is generated not only in the signal band but also in the image band, in the gain characteristics of the noise transfer function NTF(z), attenuation poles (notches) are generated at the normalized frequency±0.5 as shown in FIG. 21. In this case, even if a mismatch is created between I- and Q-channels, the image component is reduced and the reduction in SQNDR in the signal band is suppressed.    [Patent Document 1] Japanese Patent No. 3970266    [Patent Document 2] Japanese Patent No. 3992287    [Patent Document 3] Japanese Unexamined Patent Publication No. 2006-13705    [Patent Document 4] Japanese Unexamined Patent Publication No. 2006-352455    [Non-Patent Document 1] K. W. Martin: “Complex Signal Processing is Not Complex”, IEEE Trans. on Circuits Syst. I, vol. 51, no. 9, pp. 1823-1836, September 2004    [Non-Patent Document 2] Hao San, Haruo Kobayashi: “Complex Bandpass ΔΣAD Modulator with Noise-coupled Architecture”, Proceedings of IEICE General Conference on Fundamentals, A-1-9, 2008    [Non-Patent Document 3] Hao San, Haruo Kobayashi: “Complex Bandpass ΔΣAD Modulator with Noise-coupled Architecture”, Proceedings of the 21st Karuizawa Workshop on Circuits and Systems, pp. 75-80, 2008    [Non-Patent Document 4] S. Jantzi, et al.: “Quadrature bandpass ΔΣ modulator for digital radio”, IEEE Journal of Solid-State Circuits, vol. 32, p. 1935-1949, December 1997